## THERMAL SCIENCE

International Scientific Journal

### A NON-DIFFERENTIABLE SOLUTION FOR THE LOCAL FRACTIONAL TELEGRAPH EQUATION

**ABSTRACT**

In this paper, we consider the linear telegraph equations with local fractional derivative. The local fractional Laplace series expansion method is used to handle the local fractional telegraph equation. The analytical solution with the non-differentiable graphs is discussed in detail. The proposed method is efficient and accurate.

**KEYWORDS**

PAPER SUBMITTED: 2017-04-08

PAPER REVISED: 2017-06-08

PAPER ACCEPTED: 2017-06-23

PUBLISHED ONLINE: 2017-12-02

**THERMAL SCIENCE** YEAR

**2017**, VOLUME

**21**, ISSUE

**Supplement 1**, PAGES [S225 - S231]

- Yang, X. J., et al., Local Fractional Integral Transforms and Their Applications, Academic Press, New York, USA, 2015
- Mo, H., Sui, X., Generalized-Convex Functions on Fractal Sets, Abstract and Applied Analysis, 2014 (2014), ID 254737
- Saleh, W., Kilicman, A., On Generalized S-Convex Functions on Fractal Sets, JP Journal of Geometry and Topology, 17 (2015), 1, pp. 63-82
- Kilicman, A., Saleh, W., On Some Inequalities for Generalized S-Convex Functions and Applications on Fractal Sets, Journal of Nonlinear Sciences & Applications, 10 (2017), 2, pp. 583-594
- Erden, S., Sarikaya, M. Z., Generalized Pompeiu Type Inequalities for Local Fractional Integrals and Its Applications, Applied Mathematics and Computation, 274 (2016), Feb., pp. 282-291
- Sarikaya, M. Z., et al., Generalized Steffensen Inequalities for Local Fractional Integrals, International Journal of Analysis and Applications, 14 (2017), 1, pp. 88-98
- Set, E., Tomar, M., New Inequalities of Hermite-Hadamard Type for Generalized Convex Functions with Applications, Facta Universitatis, Series: Mathematics and Informatics, 31 (2016), 2, pp. 383-397
- Chen, G. S., Generalizations of Holder's and Some Related Integral Inequalities on Fractal Space, Journal of Function Spaces and Applications, 2013 (2013), ID 198405
- Liu, Q., Sun, W., A Hilbert-Type Fractal Integral Inequality and Its Applications, Journal of Inequalities and Applications, 2017 (2017), 1, pp. 83-90
- Yang, X. J., et al., On Exact Traveling-Wave Solutions for Local Fractional Korteweg-de Vries Equation, Chaos: An Interdisciplinary Journal of Nonlinear Science, 26 (2016), 8, 084312
- Yang, X. J., et al., Exact Travelling Wave Solutions for the Local Fractional Two-Dimensional Burgers- Ttype Equations, Computers and Mathematics with Applications, 73 (2017), 2, pp. 203-210
- Yang, X. J., et al., On Exact Traveling-Wave Solution for Local Fractional Boussinesq Equation in Fractal Domain, Fractals, 25 (2017), 4, 1740006
- Liu, C. F., et al., Reconstructive Schemes for Variational Iteration Method within Yang-Laplace Transform with Application to Fractal Heat Conduction Problem, Thermal Science, 17 (2013), 3, pp. 715-721
- Jafari, H., et al., A Decomposition Method for Solving Diffusion Equations via Local Fractional Time Derivative, Thermal Science, 19 (2015), Suppl. 1, pp. S123-S129
- Yang, A. M., et al., A New Coupling Schedule for Series Expansion Method and Sumudu Transform with an Applications to Diffusion Equation in Fractal Heat Transfer, Thermal Science, 19 (2015), Suppl. 1, pp. S145-S149
- Singh, J., et al., A Reliable Algorithm for a Local Fractional Tricomi Equation Arising in Fractal Transonic Flow, Entropy, 18 (2016), 6, pp. 206-214
- Baleanua, D., et al., Approximate Analytical Solutions of Goursat Problem within Local Fractional Operators, Journal of Nonlinear Sciences & Applications, 9 (2016), 6, pp. 4829-4837
- Yang, X. J., et al., A New Family of the Local Fractional PDEs, Fundamenta Informaticae, 151 (2017), 1-4, pp. 63-75
- Yang, X. J., et al., New Rheological Models within Local Fractional Derivative, Romanian Reports in Physics, 69 (2017), 3, pp. 113-124
- Yang, X. J., et al., Non-Differentiable Exact Solutions for the Nonlinear ODEs Defined on Fractal Sets, Fractals, 25 (2017), 4, 1740002
- Jafari, H., et al., On the Approximate Solutions of Local Fractional Differential Equations with Local Fractional Operators, Entropy, 18 (2016), 4, pp. 150-161
- Yan, S. P., Local Fractional Laplace Series Expansion Method for Diffusion Equation Arising in Fractal Heat Transfer, Thermal Science, 19 (2015), Suppl. 1, pp. S131-S135
- Ye, S. S., et al., The Laplace Series Solution for Local Fractional Korteweg-de Vries Equation, Thermal Science, 20 (2016), Suppl. 3, pp. S867-S870
- Yang, X. J., et al., New Analytical Solutions for Klein-Gordon and Helmholtz Equations in Fractal Dimensional Space, Proceedings of the Romanian Academy, Series A, 18 (2017), 3, pp. 231-238
- Cattani, C., et al., Fractional Dynamics, De Gruyter Open, Berlin, 2015
- Jafari, H., Jassim, H. K., Numerical Solutions of Telegraph and Laplace Equations on Cantor Sets Using Local Fractional Laplace Decomposition Method, International Journal of Advances in Applied Mathematics and Mechanics, 2 (2015), 3, pp. 144-151
- Goswami, P., Alqahtani, R. T., On the Solution of Local Fractional Differential Equations Using Local Fractional Laplace Variational Iteration Method, Mathematical Problems in Engineering, 2016 (2016), ID 9672314